Question

The cast of a play had a party at the drama teacher’s house. There were 30 cookies and 24 carrot sticks served as refreshments. Each cast member had the same number of whole cookies and the same number of whole carrot sticks. Nothing was left over. The drama teacher did not eat. How many cast members were at the party if each person had the maximum number of cookies and carrot sticks?

Answer 1

To find the number of cast members at the party with each getting the maximum whole cookies and carrot sticks, calculate the greatest common divisor (GCD) of the total cookies (30) and carrot sticks (24). The GCD is 6, indicating there were 6 cast members.

Step-by-step explanation:

The student asks how many cast members were at a party if each person had the maximum number of cookies and carrot sticks, and there were 30 cookies and 24 carrot sticks served, with nothing left over.

To solve this problem, we must find the greatest common divisor (GCD) of 30 (cookies) and 24 (carrot sticks) because the cast members had the same number of whole cookies and carrot sticks without any remainder. The greatest common divisor of 30 and 24 is 6.

Therefore, there were 30 / 6 = 5 cookies per cast member and 24 / 6 = 4 carrot sticks per cast member. Since each cast member got the same amount and we've maximized this amount by using the GCD, we can deduce that there were 6 cast members at the party. Here's the math to illustrate the process:

1. Find the GCD of 30 and 24, which is 6.
2. Divide the total number of cookies by the GCD to find the number of cookies per person: 30 / 6 = 5 cookies.
3. Divide the total number of carrot sticks by the GCD to find the number of carrot sticks per person: 24 / 6 = 4 carrot sticks.
4. The number of people is the same as the GCD, which is 6 cast members.